Least energy sign-changing solutions for nonlinear Schrödinger equations with indefinite-sign and vanishing potential

We consider the following nonlinear stationary Schrödinger equation −Δu+λV(x)u=K(x)f(u),in  RN, where N≥3N≥3, λ>0λ>0 and V(x)V(x) changes sign and may vanish at infinity. Under some suitable conditions, the least energy solution is obtained by using variational methods. Moreover, the solution changes sign when λλ is sufficiently large. Our result unifies and improves the recent one in the literature.